English

Local convexity in CAT(\kappa)-spaces

Metric Geometry 2014-09-24 v2

Abstract

Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a local property. We generalize this to CAT(0)-spaces and locally compact CAT(\kappa) spaces. As an application we give a construction of certain convex sets in euclidean buildings.

Keywords

Cite

@article{arxiv.1211.1871,
  title  = {Local convexity in CAT(\kappa)-spaces},
  author = {Kai-Uwe Bux and Stefan Witzel},
  journal= {arXiv preprint arXiv:1211.1871},
  year   = {2014}
}

Comments

13 pages, 2 figures; v2 added references

R2 v1 2026-06-21T22:34:58.810Z